Relational Methods in Computer Science pp 39-53 | Cite as

# Heterogeneous Relation Algebra

## Abstract

So far, relational algebra has been presented in its classical form. Relations are often conceived as something that might be called *quadratic* or *homogeneous*; a relation *over* a set. It is interpreted as a subset *R* ⊂ *U* × *U* of a Cartesian product of the universe *U* with itself. If relations *between* two or more sets are considered, this may easily be subsumed under this view, uniting all the sets in question into one huge set and calling this set the universe *U*. On the other hand, a variant of the theory has evolved that treats relations from the very beginning as *heterogeneous* or *rectangular*, i.e. as relations where the normal case is that they are relations between two different sets. The present chapter is devoted to this variant form.

## Keywords

Homogeneous Case Relation Algebra Bijective Mapping Surjective Homomorphism Partial Identity## Preview

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## Notes

- 1.To avoid set-theoretic problems we restrict ourselves to categories where every class of mor-phisms Mor
_{R}[*A, B*] is a set. Such categories are called locally small.Google Scholar - 2.Recall that in Chapt. 1 the small circle was used for composition of morphisms in preference to the semicolon. Here, however, we wish to emphasize that morphisms are to be thought of as relations, therefore we revert to the semicolon.Google Scholar
- 3.The universal covering got its name from a similar concept in the theory of Riemann surfaces.Google Scholar